Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21440641 | C2 | semidirect |
| 2. #21440637 | C2 | semidirect |
| 3. #21440635 | C2 | semidirect |
| 5. #21440618 | C2 | semidirect |
| 6. Q8×Dic241 | C2 | semidirect |
| 7. #21440607 | C2 | semidirect |
| 9. #21440601 | C2 | semidirect |
| 10. #21440600 | C2 | semidirect |
| 11. C22⋊Q8×C241 | C2 | semidirect |
| 72. C241 | #556 | semidirect |
| 79. C22⋊Q8 | D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440641 | 2 |
| #21440637 | 2 |
| #21440635 | 2 |
| #21440628 | 2 |
| #21440618 | 2 |
| Q8×Dic241 | 2 |
| #21440607 | 2 |
| C4×C22⋊D241 | 2 |
| #21440601 | 2 |
| #21440600 | 2 |
| C22⋊Q8×C241 | 2 |
| #556 | 241 |